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Stats Data and Models

Richard D. De Veaux, Paul F. Velleman, David E. Bock

Chapter 23

Paired Samples and Blocks - all with Video Answers

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Chapter Questions

01:35

Problem 1

Which of the following scenarios should be analyzed as paired data?
a) A group of college freshmen and a group of sophomores are asked about the quality of the university cafeteria. Do students' opinions change during their time at school?
b) Spouses are asked about the number of hours of sleep they get each night. We want to see if husbands get more sleep than wives.
c) 50 insomnia patients are given a placebo and 50 are given a mild sedative. Which subjects sleep more hours?

Kari Hasz
Kari Hasz
Numerade Educator
01:20

Problem 2

Which of the following scenarios should be analyzed as paired data?
a) Students take an MCAT prep course. Their before and after scores are compared.
b) 20 male and 20 female students in a class take a midterm. Their scores are compared.
c) A group of college freshmen are asked about the quality of the university cafeteria. A year later, the same students are asked about the cafeteria again. Do students' opinions change during their time at school?

Kari Hasz
Kari Hasz
Numerade Educator
01:45

Problem 3

We have data on the city and highway fuel efficiency of 316 cars and 316 trucks.
a) Would it be appropriate to use paired $t$ methods to compare the cars and the trucks?
b) Would it be appropriate to use paired $t$ methods to compare the city and highway fuel efficiencies of these vehicles?
c) A histogram of the differences (highway - city) is shown. Are the conditions for inference satisfied?

Kari Hasz
Kari Hasz
Numerade Educator
01:53

Problem 4

One kind of scale for weighing trucks can measure their weight as they drive across a plate. Is this method consistent with the traditional method of static weighing? Are the conditions for matched pairs inference satisfied? Weights are in $1000 \mathrm{~s}$ of pounds
$$\begin{array}{|c|c|c|}\hline \text { Weight-in-Motion } & \text { Static Weight } & \text { Diff (Static - Motion) } \\\hline 26.0 & 27.9 & -1.9 \\29.9 & 29.1 & 0.8 \\39.5 & 38.0 & 1.5 \\25.1 & 27.0 & -1.9 \\31.6 & 30.3 & 1.3 \\36.2 & 34.5 & 1.7 \\25.1 & 27.8 & -2.7 \\31.0 & 29.6 & 1.4 \\35.6 & 33.1 & 2.5 \\40.2 & 35.5 & 4.7 \\\hline\end{array}$$

Kari Hasz
Kari Hasz
Numerade Educator
02:14

Problem 5

In Exercise $3,$ after deleting an outlying value of $-27,$ the mean difference in fuel efficiencies for the 632 vehicles was $7.37 \mathrm{mpg}$ with a standard deviation of $2.52 \mathrm{mpg} .$ Find a $95 \%$ confidence interval for this difference and interpret it in context.

Michaela Flitsch
Michaela Flitsch
Numerade Educator
01:13

Problem 6

Find a $98 \%$ confidence interval of the weight differences in Exercise 4 . Interpret this interval in context.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
View

Problem 7

Thinking about the data on fuel efficiency in Exercise $3,$ why is the blocking accomplished by a matched pairs analysis particularly important for a sample that has both cars and trucks?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:31

Problem 8

Consider the weights from Exercise 4 . The side-by-side boxplots below show little difference between the two groups. Should this be sufficient to draw a conclusion about the accuracy of the weigh-in-motion scale?

James Kiss
James Kiss
Numerade Educator
05:35

Problem 9

Can a food additive increase egg production? Agricultural researchers want to design an experiment to find out. They have 100 hens available. They have two kinds of feed: the regular feed and the new feed with the additive. They plan to run their experiment for a month, recording the number of eggs each hen produces.
a) Design an experiment that will require a two-sample $t$ procedure to analyze the results.
b) Design an experiment that will require a matched-pairs $t$ procedure to analyze the results.
c) Which experiment would you consider the stronger design? Why?

Michaela Flitsch
Michaela Flitsch
Numerade Educator
02:39

Problem 10

Some students do homework with music playing in their headphones. (Anyone come to mind?) Some researchers want to see if people can work as effectively with as without distraction. The researchers will time some volunteers to see how long it takes them to complete some relatively easy crossword puzzles. During some of the trials, the room will be quiet; during other trials in the same room, subjects will wear headphones and listen to a Pandora channel.
a) Design an experiment that will require a two-sample $t$ procedure to analyze the results.
b) Design an experiment that will require a matched-pairs $t$ procedure to analyze the results.
c) Which experiment would you consider the stronger design? Why?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:08

Problem 11

Ads for many products use sexual images to try to attract attention to the product. But do these ads bring people's attention to the item that was being advertised? We want to design an experiment to see if the presence of sexual images in an advertisement affects people's ability to remember the product.
a) Describe an experiment design requiring a matched-pairs $t$ procedure to analyze the results.
b) Describe an experiment design requiring an independent sample procedure to analyze the results.

Jennifer Stoner
Jennifer Stoner
Numerade Educator
01:35

Problem 12

Many people believe that students gain weight as freshmen. Suppose we plan to conduct a study to see if this is true.
a) Describe a study design that would require a matchedpairs $t$ procedure to analyze the results.
b) Describe a study design that would require a twosample $t$ procedure to analyze the results.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
06:30

Problem 13

Values for the labor force participation rate of women (LFPR) are published by the U.S. Bureau of Labor Statistics. We are interested in whether there was a difference between female participation in 1968 and 1972, a time of rapid change for women. We check LFPR values for 19 randomly selected cities for 1968 and 1972 . Shown below is software output for two possible tests:
a) Which of these tests is appropriate for these data? Explain.
b) Using the test you selected, state your conclusion.

Michaela Flitsch
Michaela Flitsch
Numerade Educator
02:57

Problem 14

Simpson, Alsen, and Eden (Technometrics 1975 ) report the results of trials in which clouds were seeded and the amount of rainfall recorded. The authors report on 26 seeded and 26 unseeded clouds in order of the amount of rainfall, largest amount first. Here are two possible tests to study the question of whether cloud seeding works.
Paired t-Test of $\mu(1-2)$ Mean of Paired Differences $=-277.39615$ t-Statistic $=-3.641$ with $25 \mathrm{df}$
$p=0.0012$
2-Sample t-Test of $\mu 1-\mu 2$ Difference Between Means $=-277.4$ t-Statistic $=-1.998$ with $33 \mathrm{df}$
$p=0.0538$
a) Which of these tests is appropriate for these data? Explain.
b) Using the test you selected, state your conclusion.

Teresa Wray
Teresa Wray
Numerade Educator
04:50

Problem 15

The British Medical Journal published an article titled, "Is Friday the 13 th Bad for Your Health?" Researchers in Britain examined how Friday the 13 th affects human behavior. One question was whether people tend to stay at home more on Friday the 13 th. The data below are the number of cars passing Junctions 9 and 10 on the M25 motorway for consecutive Fridays (the 6 th and 13 th ) for five different periods.
$$\begin{array}{|l|l|c|c|}\hline \text { Year } & \multicolumn{1}{|c|} {\text { Month }} & \text { 6th } & \multicolumn{1}{|c|} {13 \text { th }} \\
\hline 1990 & \text { July } & 134,012 & 132,908 \\
1991 & \text { September } & 133,732 & 131,843 \\
1991 & \text { December } & 121,139 & 118,723 \\
1992 & \text { March } & 124,631 & 120,249 \\
1992 & \text { November } & 117,584 & 117,263 \\
\hline\end{array}$$
a) Which of the tests is appropriate for these data? Explain.
b) Using the test you selected, state your conclusion.
c) Are the assumptions and conditions for inference met?

Teresa Wray
Teresa Wray
Numerade Educator
04:49

Problem 16

The researchers in Exercise 15 also examined the number of people admitted to emergency rooms for vehicular accidents on 12 Friday evenings ( 6 each on the 6 th and 13 th ).
$$\begin{array}{|l|l|r|r|}
\hline \text { Year } & \multicolumn{1}{|c|} {\text { Month }} & \multicolumn{1}{|c|} {\text { 6th }} & \multicolumn{1}{|c{13 \text { th }} \\\hline 1989 & \text { October } & 9 & 13 \\
1990 & \text { July } & 6 & 12 \\
1991 & \text { September } & 11 & 14 \\
1991 & \text { December } & 11 & 10 \\
1992 & \text { March } & 3 & 4 \\
1992 & \text { November } & 5 & 12 \\\hline\end{array}$$
Based on these data, is there evidence that more people are admitted, on average, on Friday the 13 th? Here are two possible analyses of the data:
a) Which of these tests is appropriate for these data? Explain.
b) Using the test you selected, state your conclusion.
c) Are the assumptions and conditions for inference met?

Teresa Wray
Teresa Wray
Numerade Educator
01:31

Problem 17

After seeing countless commercials claiming one can get cheaper car insurance from an online company, a local insurance agent was concerned that he might lose some customers. To investigate, he randomly selected profiles (type of car, coverage, driving record, etc.) for 10 of his clients and checked online price quotes for their policies. The comparisons are shown in the table below. His statistical software produced the following summaries (where PriceDiff $=$ Local $-$ Online ):$$\begin{array}{lccc}
\text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } \\
\text { Local } & 10 & 799.200 & 229.281 \\
\text { Online } & 10 & 753.300 & 256.267 \\
\text { PriceDiff } & 10 & 45.9000 & 175.663\end{array}$$
$$
\begin{array}{r|r|r}
\text { Local } & \text { Online } & \text { PriceDiff } \\\hline 568 & 391 & 177 \\
872 & 602 & 270 \\
451 & 488 & -37 \\1229 & 903 & 326 \\
605 & 677 & -72 \\1021 & 1270 & -249 \\
783 & 703 & 80 \\844 & 789 & 55 \\
907 & 1008 & -101 \\
712 & 702 & 10\end{array}$$
At first, the insurance agent wondered whether there was some kind of mistake in this output. He thought the Pythagorean Theorem of Statistics should work for finding the standard deviation of the price differencesin other words, that
$S D($ Local $-$ Online $)=\sqrt{S D^{2}(\text { Local })+S D^{2}(\text { Online })}$
But when he checked, he found that $\sqrt{(229.281)^{2}+(256.267)^{2}}=343.864,$ not 175.663
as given by the software. Tell him where his mistake is.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:16

Problem 18

To select the site for an electricity generating wind turbine, wind speeds were recorded at several potential sites every 6 hours for a year. Two sites not far from each other looked good. Each had a mean wind speed high enough to qualify, but we should choose the site with a higher average daily wind speed. Because the sites are near each other and the wind speeds were recorded at the same times, we should view the speeds as paired. Here are the summaries of the speeds (in miles per hour):
$$\begin{array}{l|c|c|c|}
\hline \text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } \\
\hline \text { site2 } & 1114 & 7.452 & 3.586 \\
\text { site4 } & 1114 & 7.248 & 3.421 \\
\text { site2 - site4 } & 1114 & 0.204 & 2.551 \\\hline\end{array}$$
Is there a mistake in this output? Why doesn't the Pythagorean Theorem of Statistics work here? In other words, shouldn't
$$S D(\text { site } 2-\text { site } 4)=\sqrt{S D^{2}(\text { site } 2)+S D^{2}(\text { site4 })} ?$$
But $\sqrt{(3.586)^{2}+(3.421)^{2}}=4.956,$ not 2.551 as given by the software. Explain why this happened.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:48

Problem 19

In Exercise $17,$ we saw summary statistics for 10 drivers' car insurance premiums quoted by a local agent and an online company. Here are displays for each company's quotes and for the difference $($ Local $-$ Online $):$
a) Which of the summaries would help you decide whether the online company offers cheaper insurance? Why?
b) The standard deviation of PriceDiff is quite a bit smaller than the standard deviation of prices quoted by either the local or online companies. Discuss why.
c) Using the information you have, discuss the assumptions and conditions for inference with these data.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:38

Problem 20

In Exercise 18 , we saw summary statistics for wind speeds at two sites near each other, both being considered as locations for an electricitygenerating wind turbine. The data, recorded every 6 hours for a year, showed each of the sites had a mean wind speed high enough to qualify, but how can we tell which site is best? Here are some displays: a) The boxplots show outliers for each site, yet the histogram shows none. Discuss why.
b) Which of the summaries would you use to select between these sites? Why?
c) Using the information you have, discuss the assumptions and conditions for paired $t$ inference for these data. (Hint: Think hard about the independence assumption in particular.)

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:45

Problem 21

Exercises 17 and 19 give summaries and displays for car insurance premiums quoted by a local agent and an online company. Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to the online company.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:16

Problem 22

Exercises 18 and 20 give summaries and displays for two potential sites for a wind turbine. Test an appropriate hypothesis to see if there is evidence that either of these sites has a higher average wind speed.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:42

Problem 23

The following table gives the average daily high temperatures in January and July for several cities. Find a $95 \%$ confidence interval for the mean temperature difference between summer and winter.
a) Check the assumptions and conditions. If you find a city that doesn't belong with the others, set it aside.
b) Compute your interval for the data (adjusted, if necessary), and explain what it means.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
01:46

Problem 24

The table below shows the winning times (in minutes) for men and women in the New York City Marathon between 1978 and 2013. (The race was not run in 2012 because of Superstorm Sandy.). Assuming that performances in the Big Apple resemble performances elsewhere, we can think of these data as a sample of performance in marathon competitions. Create a $90 \%$ confidence interval for the mean difference in winning times for male and female marathon competitors. (www.nycmarathon.org)
$$\begin{array}{|c|c|c|c|c|c|}
\hline \text { Year } & \text { Men } & \text { Women } & \text { Year } & \text { Men } & \text { Women } \\
\hline 1978 & 132.2 & 152.5 & 1996 & 129.9 & 148.3 \\
1979 & 131.7 & 147.6 & 1997 & 128.2 & 148.7 \\
1980 & 129.7 & 145.7 & 1998 & 128.8 & 145.3 \\
1981 & 128.2 & 145.5 & 1999 & 129.2 & 145.1 \\
1982 & 129.5 & 147.2 & 2000 & 130.2 & 145.8 \\
1983 & 129.0 & 147.0 & 2001 & 127.7 & 144.4 \\
1984 & 134.9 & 149.5 & 2002 & 128.1 & 145.9 \\
1985 & 131.6 & 148.6 & 2003 & 130.5 & 142.5 \\
1986 & 131.1 & 148.1 & 2004 & 129.5 & 143.2 \\
1987 & 131.0 & 150.3 & 2005 & 129.5 & 144.7 \\
1988 & 128.3 & 148.1 & 2006 & 130.0 & 145.1 \\
1989 & 128.0 & 145.5 & 2007 & 129.1 & 143.2 \\
1990 & 132.7 & 150.8 & 2008 & 128.7 & 143.9 \\
1991 & 129.5 & 147.5 & 2009 & 129.3 & 148.9 \\
1992 & 129.5 & 144.7 & 2010 & 128.3 & 148.3 \\
1993 & 130.1 & 146.4 & 2011 & 125.1 & 143.3 \\
1994 & 131.4 & 147.6 & 2012 & {<\text { cancelled }>} \\
1995 & 131.1 & 148.1 & 2013 & 128.4 & 140.1
\end{array}$$

James Kiss
James Kiss
Numerade Educator
01:52

Problem 25

Every year, the students at Gossett High School take a physical fitness test during their gym classes. One component of the test asks them to do as many push-ups as they can. Results for one class are shown below, separately for boys and girls. Assuming that students at Gossett are assigned to gym classes at random, create a $90 \%$ confidence interval for how many more push-ups boys can do than girls, on average, at that high school.
$$\begin{array}{|l|l|r|l|l|r|r|r|r|r|r|r|r|}
\hline \text { Boys } & 17 & 27 & 31 & 17 & 25 & 32 & 28 & 23 & 25 & 16 & 11 & 34 \\
\hline \text { Girls } & 24 & 7 & 14 & 16 & 2 & 15 & 19 & 25 & 10 & 27 & 31 & 8 \\
\hline\end{array}$$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:49

Problem 26

An experiment was performed to see whether sensory deprivation over an extended period of time has any effect on the alpha-wave patterns produced by the brain. To determine this, 20 subjects, inmates in a Canadian prison, were randomly split into two groups. Members of one group were placed in solitary confinement. Those in the other group were allowed to remain in their own cells. Seven days later, alpha-wave frequencies were measured for all subjects, as shown in the following table. (Source:
P. Gendreau et al., "Changes in EEG Alpha Frequency and
Evoked Response Latency During Solitary Confinement,"
$$\begin{array}{|c|c|}\hline \text { Nonconfined } & \text { Confined } \\\hline 10.7 & 9.6 \\
10.7 & 10.4 \\10.4 & 9.7 \\10.9 & 10.3 \\10.5 & 9.2 \\10.3 & 9.3 \\
9.6 & 9.9 \\11.1 & 9.5 \\11.2 & 9.0 \\10.4 & 10.9 \\\hline\end{array}$$
a) What are the null and alternative hypotheses? Be sure to define all the terms and symbols you use.
b) Are the assumptions necessary for inference met?
c) Perform the appropriate test, indicating the formula you used, the calculated value of the test statistic, the df, and the P-value.
d) State your conclusion.

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:53

Problem 27

(When you first read about this exercise break plan in Chapter 22, you did not have an inference method that would work. Try again now.) A company institutes an exercise break for its workers to see if it will improve job satisfaction, as measured by a questionnaire that assesses workers' satisfaction. Scores for 10 randomly selected workers before and after the implementation of the exercise program are shown in the table below.
a) Identify the procedure you would use to assess the effectiveness of the exercise program, and check to see if the conditions allow the use of that procedure.
b) Test an appropriate hypothesis and state your conclusion.
c) If your conclusion turns out to be incorrect, what kind of error did you commit?
"d) Use a matched-pairs sign test to test the appropriate hypothesis. Do your conclusions change from those in part b?
$$\begin{array}{|c|c|c|}
\hline \text { Worker } {\text { Job Satisfaction Index }} \\
\text { Number } & \text { Before } & \text { After } \\
\hline 1 & 34 & 33 \\
2 & 28 & 36 \\
3 & 29 & 50 \\
4 & 45 & 41 \\
5 & 26 & 37 \\
6 & 27 & 41 \\
7 & 24 & 39 \\
8 & 15 & 21 \\
9 & 15 & 20 \\
10 & 27 & 37 \\
\hline\end{array}$$

Sheryl Ezze
Sheryl Ezze
Numerade Educator
02:34

Problem 28

(When you first read about the summer school issue in Chapter 22, you did not have an inference method that would work. Try again now.) Having done poorly on their Math final exams in June, six students repeat the course in summer school and take another exam in August.
$$\begin{array}{|r|r|r|r|r|r|r|}
\hline \text { June } & 54 & 49 & 68 & 66 & 62 & 62 \\
\hline \text { Aug. } & 50 & 65 & 74 & 64 & 68 & 72 \\
\hline\end{array}$$
a) If we consider these students to be representative of all students who might attend this summer school in other years, do these results provide evidence that the program is worthwhile?
b) This conclusion, of course, may be incorrect. If so, which type of error was made?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
06:54

Problem 29

Is there a significant difference in calories between servings of strawberry and vanilla yogurt? Based on the data shown in the table, test an appropriate hypothesis and state your conclusion. Don't forget to check assumptions and conditions!
$$\begin{array}{l|c|c}\hline & {\text { Calories per Serving }} \\
\text { Brand } & \text { Strawberry } & \text { Vanilla } \\
\hline \text { America's Choice } & 210 & 200 \\
\text { Breyer's Lowfat } & 220 & 220 \\\text { Columbo } & 220 & 180 \\\text { Dannon Light'n Fit } & 120 & 120 \\\text { Dannon Lowfat } & 210 & 230 \\\text { Dannon la Crème } & 140 & 140 \\\text { Great Value } & 180 & 80 \\\text { La Yogurt } & 170 & 160 \\
\text { Mountain High } & 200 & 170 \\\text { Stonyfield Farm } & 100 & 120 \\
\text { Yoplait Custard } & 190 & 190 \\\text { Yoplait Light } & 100 & 100\end{array}$$

Michaela Flitsch
Michaela Flitsch
Numerade Educator
06:02

Problem 30

Many drivers of cars that can run on regular gas actually buy premium in the belief that they will get better gas mileage. To test that belief, we use 10 cars from a company fleet in which all the cars run on regular gas. Each car is filled first with either regular or premium gasoline, decided by a coin toss, and the mileage for that tankful is recorded. Then the mileage is recorded again for the same cars for a tankful of the other kind of gasoline. We don't let the drivers know about this experiment.
Here are the results (miles per gallon):
$$\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|}
\hline \text { Car # } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline \text { Regular } & 16 & 20 & 21 & 22 & 23 & 22 & 27 & 25 & 27 & 28 \\
\hline \text { Premium } & 19 & 22 & 24 & 24 & 25 & 25 & 26 & 26 & 28 & 32 \\
\hline\end{array}$$
a) Is there evidence that cars get significantly better fuel economy with premium gasoline?
b) How big might that difference be? Check a $90 \%$ confidence interval.
c) Even if the difference is significant, why might the company choose to stick with regular gasoline?
d) Suppose you had done a "bad thing." (We're sure you didn't.) Suppose you had mistakenly treated these data as two independent samples instead of matched pairs. What would the significance test have found? Carefully explain why the results are so different.
*e) Use a matched-pairs sign test to test the appropriate hypothesis. Do your conclusions change from those in part a?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
07:26

Problem 31

A tire manufacturer tested the braking performance of one of its tire models on a test track. The company tried the tires on 10 different cars, recording the stopping distance for each car on both wet and dry pavement. Results are shown in the table. a) Write a $95 \%$ confidence interval for the mean dry pavement stopping distance. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.
b) Write a $95 \%$ confidence interval for the mean increase in stopping distance on wet pavement. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.

Michaela Flitsch
Michaela Flitsch
Numerade Educator
02:30

Problem 32

For another test of the tires in Exercise 31 , a car made repeated stops from 60 miles per hour. The test was run on both dry and wet pavement, with results as shown in the table. (Note that actual braking distance, which takes into account the driver's reaction time, is much longer, typically nearly 300 feet at $60 \mathrm{mph} !$ )
a) Write a $95 \%$ confidence interval for the mean dry pavement stopping distance. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.
b) Write a $95 \%$ confidence interval for the mean increase in stopping distance on wet pavement. Be sure to check the appropriate assumptions and conditions, and explain what your interval means.
$$\begin{array}{|c|c|}
\hline {\text { Stopping Distance (ft) }} \\\begin{array}{c}
\text { Dry } \\\text { Pavement }\end{array} & \begin{array}{c}\text { Wet } \\\text { Pavement }
\end{array} \\\hline 145 & 211 \\152 & 191 \\141 & 220 \\143 & 207 \\131 & 198 \\
148 & 208 \\126 & 206 \\140 & 177 \\135 & 183 \\
133 & 223 \\\hline\end{array}$$

Lynn Larson
Lynn Larson
Numerade Educator
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Problem 33

How much more do public colleges and universities charge out-of-state students for tuition per year? A random sample of 19 public colleges and universities listed at www.collegeboard.com yielded the following data for students entering as Freshmen in Fall $2013 .$ a) Create a $90 \%$ confidence interval for the mean difference in cost. Be sure to justify your procedure.
b) Interpret your interval in context.
c) A national magazine claims that public institutions charge state residents an average of $\$ 7000$ less than out-of-staters for tuition each year. What does your confidence interval indicate about this assertion?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
View

Problem 34

In Exercise $11,$ you considered the question of whether sexual images in ads affected people's abilities to remember the item being advertised. To investigate, a group of Statistics students cut ads out of magazines. They were careful to find two ads for each of 10 similar items, one with a sexual image and one without. They arranged the ads in random order and had 39 subjects look at them for one minute. Then they asked the subjects to list as many of the products as they could remember. Their data are shown in the table. Is there evidence that the sexual images mattered?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
View

Problem 35

Advertisements for an instructional video claim that the techniques will improve the ability of Little League pitchers to throw strikes and that, after undergoing the training, players will be able to throw strikes on at least $60 \%$ of their pitches. To test this claim, we have 20 Little Leaguers throw 50 pitches each, and we record the number of strikes. After the players participate in the training program, we repeat the test. The table (on the next page) shows the number of strikes each player threw before and after the training.
a) Is there evidence that after training players can throw strikes more than $60 \%$ of the time?
b) Is there evidence that the training is effective in improving a player's ability to throw strikes?
c) Use a matched-pairs sign test to test the appropriate hypothesis. Do your conclusions change from those in part a?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:11

Problem 36

In Exercise $12,$ you thought about how to design a study to see if it's true that students tend to gain weight during their first year in college. Well, Cornell Professor of Nutrition David Levitsky did just that. He recruited students from two large sections of an introductory health course. Although they were volunteers, they appeared to match the rest of the freshman class in terms of demographic variables such as sex and ethnicity. The students were weighed during the first week of the semester, then again 12 weeks later. Based on Professor Levitsky's data, estimate the mean weight gain in first-semester freshmen and comment on the "freshman 15." (Weights are in pounds.)

James Kiss
James Kiss
Numerade Educator
04:18

Problem 37

The Boston Marathon has had a wheelchair division since $1977 .$ Who do you think is typically faster, the men's marathon winner on foot or the women's wheelchair marathon winner? Because the conditions differ from year to year, and speeds have improved over the years, it seems best to treat these as paired measurements. Here are summary statistics for the pairwise differences in finishing time (in minutes):
(www.boston.com/sports/marathon/history/champions/)
c) Would a hypothesis test at $\alpha=0.05$ reject the null hypothesis of no difference? What conclusion would you draw?

John Piaszynski
John Piaszynski
Numerade Educator
01:36

Problem 39

Many dairy cows now receive injections of BST, a hormone intended to spur greater milk production. After the first injection, a test herd of 61 Ayrshire cows increased their mean daily production from 47 pounds to 57 pounds of milk. The standard deviation of the increases was 3.1 pounds. We want to estimate the mean increase a farmer could expect in his own cows.
a) Check the assumptions and conditions for inference.
b) Write a $95 \%$ confidence interval.
c) Explain what your interval means in this context.
d) Given the cost of $\mathrm{BST}$, a farmer believes he cannot afford to use it unless he is sure of attaining at least a $25 \%$ increase in milk production. Based on your confidence interval, what advice would you give him?

Hoan Nguyen
Hoan Nguyen
Numerade Educator
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Problem 40

In the experiment about hormone injections in cows described in Exercise $39,$ a group of 52 Jersey cows increased average milk production from 43 pounds to 52 pounds per day, with a standard deviation of 4.8 pounds. Is this evidence that the hormone may be more effective in one breed than the other? Test an appropriate hypothesis and state your conclusion. Be sure to discuss any assumptions you make.

Rashmi Sinha
Rashmi Sinha
Numerade Educator